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2 years ago

Please put answer as a mixed number! :) 1 and 3/8* 1.5 + 5 and 5/8 ÷ 0.4 =

Mathematics

1 answer:

Natasha_Volkova [10]2 years ago

8 0

Answer: 7 1/16 and 1 9/16

Step-by-step explanation: 1 3/8 x 1.5 is 1 3/8 x 1 5/10 11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16. We add 5 to get 7 1/16.

5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.

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If a ball is thrown in the air with a velocity 52 ft/s, its height in feet t seconds later is given by y = 52t - 16t^2. Find the

Sunny_sXe [5.5K]

Answer:

a.) -20ft/s

b.) -13.6ft/s

c.) -12.8ft/s

d.) -12.16ft/s

e.) -12ft/s

Step-by-step explanation:

Average Velocity = Change in distance/change in time.

Distance from the question in given in form of t as y= 52t - 16t² If our initial time is 2, distance travelled at t=2 is given as

Y(2) = 52(2) - 16(2)² =104 - 64

Y = 40ft.

For question a, when change In t is 0.5 seconds, that is from 2 sec to 2.5 seconds,

Average velocity = y(2.5) - y(2)/0.5

y(2.5) = 52(2.5) - 16(2.5)² =130 - 100 = 30

Y(2) = 40

Average velocity in 0.5 seconds = [30 - 40]/0.5 = -20ft/s.

For question b, when change In t is 0.1 seconds, that is from 2 sec to 2.1 seconds,

Average velocity = y(2.1) - y(2)/0.1

y(2.1) = 52(2.1) - 16(2.1)² =109.2 - 70.56= 38.64

Y(2) = 40,

Average velocity in 0.1 seconds = [38.64 - 40]/0.1 = -13.6ft/s.

For question c, when change In t is 0.05 seconds, that is from 2 sec to 2.05 seconds,

Average velocity = y(2.05) - y(2)/0.05

y(2.05) = 52(2.05) - 16(2.05)² = 106.6 - 67.24 = 39.36

Y(2) = 40

Average velocity in 0.05 seconds = [39.36 - 40]/0.05 = -12.8ft/s.

For question d, when change In t is 0.01 seconds, that is from 2 sec to 2.01 seconds,

Average velocity = y(2.01) - y(2)/0.01

y(2.01) = 52(2.01) - 16(2.01)² = 104.52 -64.6416 = 39.8784

Y(2) = 40

Average velocity in 0.5 seconds = [39.8784 - 40]/0.01 = -12.16ft/s.

Instantaneous velocity at t =2 is derived by getting the first derivative of y and inserting Our value of t=2 into the first derivative.

If y = 52t - 16t², then derivative of y becomes y' given as

y'= 52 - 32t

At t = 2,

y'= 52 - 32(2) = 52 - 64 = - 12ft/s.

Instantaneous velocity at t=2 is given as -12ft/s.

5 0

3 years ago

Find chase's mistake

alekssr [168]

This is no mistake he is the one

7 0

3 years ago

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

9966 [12]

Answer:

$(a)\ Area = 3765.32$

$(b)\ Area = 4773$

Step-by-step explanation:

Given

$A_1 = 169in^2$ --- area of each square

$Shade = 4in$

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

$L^2 = A_1$

$L^2 = 169$

$L = \sqrt{169$

$L=13$

The length of two squares make up the radius of the semicircle.

So:

$r = 2 * L$

$r = 2*13$

$r = 26$

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

$A_2 = 16 * 169$

$A_2 = 2704$

The area of the semicircle is:

$A_3 = \frac{\pi r^2}{2}$

$A_3 = \frac{3.14 * 26^2}{2}$

$A_3 = 1061.32$

So, the area of the window is:

$Area = A_2 + A_3$

$Area = 2704 + 1061.32$

$Area = 3765.32$

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

$Length = 60$

$Height = 4*13 + 4$

$Height = 56$

The area is:

$A_1 = 60 * 56 = 3360$

The radius of the semicircle becomes initial radius + 4

$r = 26 + 4 = 30$

The area is:

$A_2 = \frac{3.14 * 30^2}{2} = 1413$

The area of the shade is:

$Area = A_1 + A_2$

$Area = 3360 + 1413$

$Area = 4773$

7 0

3 years ago

A grocery store orders 47 bags of onins and 162 bags of potatoes. The onions cost 2 per bag , and potatoes cost 3 per bag How mu

Alina [70]

Answer:

580 is spent on onions and potatoes

Step-by-step explanation:

The grocery store ordered 47 bags of onions, and 1 bag costs 2.

It also ordered 167 bags of potatoes, and the bag costs 3.

47 bags onions X 2 render 94

162 bags potatoes X 3 render 486

94 (cost of onions) + 486 (cost of potatoes) = 580

7 0

4 years ago

Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 1

liubo4ka [24]

Answer:

a) P (A)= 88/102= 0.8627

(b) P (B)= 89/102= 0.8725

c) P (A`) = 14/102 = 0.1372

(d) P (A∩B) = 84/102 =0.8235

(e) P(AUB)= 93/102 = 0.9117

(f)P (A`UB) = 98/102= 0.96078

Step-by-step explanation:

edge

finish excellent good Total

<u>(A )surface finish excellent 84 4 88</u>

good ( B) ⇵ 5 9 14

Total 89 13 102

a) Upper P left-parenthesis Upper A right-parenthesis equals

P (A)= 88/102= 0.8627

All the elements of set A = 84+4= 88

(b) Upper P left-parenthesis Upper B right-parenthesis equals

P (B)= 89/102= 0.8725

All the elements of set B = 84+5= 89

c) Upper P left-parenthesis Upper A prime right-parenthesis equal

P (A`) = 14/102 = 0.1372

All the elements of Universal set U which are not elements of set A = 102- 88= 14

(d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equals

P (A∩B) = 84/102 =0.8235

Only those elements of set A and set B which are common

(e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equals

P(AUB)= 93/102 = 0.9117

Totalling elements of set A and B= 88+5= 93

(f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equals

P (A`UB) = 98/102= 0.96078

All the elements of Universal set U which are not elements of set A and the elements of Set B = 5+9+ 84= 98

6 0

3 years ago